PHYSICS 313
Problem set 6 2002
Given Nov 18
Due Nov 27

Problem 1: The latent heat of melting ice is 80 Kcal kg$^{-1}$ at atmospheric pressure. The melting temperature is 273 K and the the density of ice is 917 kg m$^{-3}$, while the density of water can be taken to be 1000 kg m$^{-3}$. Estimate the change in melting temperature if the pressure is increased to 100 bar.
Problem 2:
a: Estimate the difference in chemical potential $\mu_l-\mu_g$ of the gas and liquid phases of water at 300K if the relative humidity is 110%.
b: Estimate the radius of a water droplet for which the excess Gibbs free energy

$$(\mu_l-\mu_g)\frac{v}{v_l}+\sigma A$$

has a maximum. (Droplets above this size will grow in pure air, while smaller droplets will evaporate.)
Problem 3:
a: The entropy at oxygen gas at $T=298$ K and atmospheric pressure is 205.14 J K$^{-1}$ mol$^{-1}$. Estimate the chemical potential of oxygen under these conditions.
b: The surface of a container with oxygen at 298 K, 1 atm. pressure contains discrete absorption sites at which oxygen molecules may be bound. These sites may be either occupied by an oxygen molecule or empty. Assume that there are N such sites on the surface, that the internal energy of an occupied site is $\epsilon$, that the internal energy of an empty site is zero and that the fraction of sites that are occupied is $x$. Find the entropy of the absorption sites.
c: What is the chemical potential of the absorbed oxygen under the conditions in part b?
d: Assume that the chemical potentials of absorbed and gas phase oxygen are the same and that $\epsilon=-0.4$ electron volt. What is the fraction $x$ of sites that are occupied?